What is 1/2 ln((1+1/(sqrt(2)))/(1-1/(sqrt(2)))) ?

The solution to 1/2 ln((1+1/(sqrt(2)))/(1-1/(sqrt(2)))) is 1/2 (ln(1+(sqrt(2))/2)-ln(1-(sqrt(2))/2))

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simplify 1/2 ln((1+1/(sqrt(2)))/(1-1/(sqrt(2))))

simplify

\frac{1}{2} ln (\frac{1 + \frac{1}{2}}{1 - \frac{1}{2}})

\frac{1}{2} (ln (1 + \frac{2}{2}) - ln (1 - \frac{2}{2}))

Decimal Notation

0.88137 \dots

Solution steps

\frac{1}{2} ln (\frac{1 + \frac{1}{2}}{1 - \frac{1}{2}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{1 + \frac{1}{2}}{1 - \frac{1}{2}}) = ln (1 + \frac{1}{2}) - ln (1 - \frac{1}{2})

= \frac{1}{2} (ln (\frac{1}{2} + 1) - ln (- \frac{1}{2} + 1))

\frac{1}{2} = \frac{2}{2}

= \frac{1}{2} (ln (\frac{2}{2} + 1) - ln (- \frac{1}{2} + 1))

\frac{1}{2} = \frac{2}{2}

= \frac{1}{2} (ln (\frac{2}{2} + 1) - ln (- \frac{2}{2} + 1))

ln (3 ab \cdot 5 c)

lo g_{a} (\frac{m}{n})

lo g_{10} (x) + lo g_{10} (x^{2} y) + 3 lo g_{10} (y)

lo g_{10} (\frac{z ^{3}}{x ^{5} y})

ln (x sin (x))

What is 1/2 ln((1+1/(sqrt(2)))/(1-1/(sqrt(2)))) ?
The solution to 1/2 ln((1+1/(sqrt(2)))/(1-1/(sqrt(2)))) is 1/2 (ln(1+(sqrt(2))/2)-ln(1-(sqrt(2))/2))